论文标题
扭曲的模量空间和Duistermaat-Heckman措施
Twisted Moduli Spaces and Duistermaat-Heckman Measures
论文作者
论文摘要
在Boalch-Yamakawa和Meinrenken之后，我们考虑了从准哈米尔顿的角度来考虑在边界表面上的某些模量空间。对于给定的Lie Group $ G $，这些字符品种在“扭曲”本地系统上参数flat $ g $ - 连接，因为过渡函数在$ g \ rtimes \ rtimes \ mathrm {aut}（g）$中取值。在审查了讨论扭曲的准哈米尔顿流形的必要工具之后，我们在$ g $上构建了一个duistermaat-Heckman（DH）量度，该测量是在扭曲的共轭动作$ g \ g \ mapstohgκ（h^{-1}）$下不变的，用于$κ\ in \ nrm fy \ mathrm {g）$ {然后，我们通过确定扭曲模量空间的DH度量来说明我们的结果。
Following Boalch-Yamakawa and Meinrenken, we consider a certain class of moduli spaces on bordered surfaces from a quasi-Hamiltonian perspective. For a given Lie group $G$, these character varieties parametrize flat $G$-connections on "twisted" local systems, in the sense that the transition functions take values in $G\rtimes\mathrm{Aut}(G)$. After reviewing the necessary tools to discuss twisted quasi-Hamiltonian manifolds, we construct a Duistermaat-Heckman (DH) measure on $G$ that is invariant under the twisted conjugation action $g\mapsto hgκ(h^{-1})$ for $κ\in\mathrm{Aut}(G)$, and characterize it by giving a localization formula for its Fourier coefficients. We then illustrate our results by determining the DH measures of our twisted moduli spaces.
